Methods for selecting intraocular lenses and relaxing incisions for correcting refractive error

ABSTRACT

The disclosure provides a method for selecting toric intraocular lenses (IOL) and relaxing incision for correcting refractive error. The one or more toric IOL and relaxing incision combinations can be used for off-axis correction of refractive errors such as astigmatism. The disclosure provides a method for selecting toric IOL and relaxing incision combinations that have combined astigmatism correcting powers and off-axis positions or orientations of the astigmatism correcting axes of the toric IOL and relaxing incision that are effective to yield lower residual astigmatism than on axis correction methods. The toric IOL and relaxing incision combinations also allow the user to avoid incisions that will radially overlap with a cataract incision thereby provided improved outcomes.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. non-provisional applicationSer. No. 15/131,713, filed Apr. 18, 2016, which claims priority to U.S.provisional application No. 62/149,539 filed Apr. 18, 2015, the contentsof which is incorporated herein by reference in its entirety.

BACKGROUND

Astigmatism results from refractive errors caused by an asymmetric orirregularly shaped cornea or changes in the curvature of the lens insidethe eye affecting the bending or refraction of light in the eye.Astigmatism usually causes blurred or distorted vision at all distancesand where uncorrected, can lead to eyestrain, headaches and fatigue withprolonged visual tasks. It has been reported that up to 95% of eyes havesome amount of astigmatism, with more than 28% of children between theages of 5 to 17 and about 15% to 30% of adults have astigmatism of 1diopter or greater. See J. B. Rubenstein, Today's Peripheral CornealRelaxing incision, in Cataract & Refractive Surgery Today, pages 26-28,May 2014.

Astigmatism can be corrected during cataract surgery by placing thenatural lens with a correcting toric intraocular lens (IOL) or throughrelaxing the curvature of the cornea by making paired arcuate incisionsin the limbus or cornea of the eye using procedures such as limbalrelaxing incision (LRI), astigmatic keratotomy (AK) or femtosecond laserassisted astigmatic keratotomy (fAK). These act to compensate for thecorneal astigmatism and astigmatism resulting from the cataractincision(s). Current methods to correct astigmatism have limitedeffectiveness, as use of relaxing incisions is not always possible dueto interfering cataract incisions, and both relaxing incision and toricIOLs usually provide only discrete astigmatism correcting power.

SUMMARY OF THE INVENTION

The present disclosure provides methods, tools, and systems forselecting intraocular lens useful for correcting astigmatism. Themethods, tools and systems of embodiments of the invention are notlimited by the discrete astigmatism correcting power of existing toricIOLs, alignment with the main axis of astigmatism to be corrected, orthe position of interfering cataract incisions.

In one aspect, the invention provides a method for selecting a toricintraocular lens (IOL) and a relaxing incision combination effective tocorrect astigmatism when the toric IOL is implanted in an eye in a firstoff-axis orientation in combination with placement of the relaxingincision in a second off-axis position. The method involves: (a)receiving a predetermined magnitude for the astigmatism to be corrected;and (b) identifying a toric IOL-relaxing incision combination, whereinthe toric IOL has a first astigmatism correcting power and the relaxingincision has a second astigmatism correcting power, the combination ofany two of the first astigmatism correcting power, the secondastigmatism correcting power, and the magnitude of astigmatism beingcorrected is greater than the first astigmatism correcting power, thesecond astigmatism correcting power, or the magnitude of astigmatism notin the combination.

In some embodiments, the astigmatism to be corrected includes surgicallyinduced astigmatism. In some embodiments, the first astigmatismcorrecting power is the astigmatism correcting power of the IOL at thecorneal plane. In some embodiments, the astigmatism correcting power ofthe IOL at the corneal plane is determined using anatomical distanceswithin the eye. In some embodiments, the toric IOL is further selectedbased on residual sphere value, residual astigmatism value, the index ofrefraction of the IOL, or any combination thereof. In some embodiments,the first astigmatism correcting power or the second astigmatismcorrecting power is about 0.25, about 0.5, about 0.75, about 1, about1.25, about 1.5, about 1.75, about 2, about 2.25, about 2.5, about 2.75,about 3, about 3.25, about 3.5, about 3.75, about 4, about 4.25, about4.5, about 4.75, about 5, about 5.25, about 5.5, about 5.75, about 6,about 6.25, about 6.5, about 6.75, about 7, about 7.25, about 7.5, about7.75, about 8, about 8.25, about 8.5, about 8.75, about 9, about 9.25,about 9.5, about 9.75, or about 10 diopters. In some embodiments, eachof the first and second astigmatism correcting power is about 0.25,about 0.5, about 0.75, about 1, about 1.25, about 1.5, about 1.75, about2, about 2.25, about 2.5, about 2.75, about 3, about 3.25, about 3.5,about 3.75, about 4, about 4.25, about 4.5, about 4.75, about 5, about5.25, about 5.5, about 5.75, about 6, about 6.25, about 6.5, about 6.75,about 7, about 7.25, about 7.5, about 7.75, about 8, about 8.25, about8.5, about 8.75, about 9, about 9.25, about 9.5, about 9.75, or about 10diopters.

In some embodiments, the method includes identifying the off-axisorientation of the toric IOL by determining the position of theastigmatism-correcting axis of the IOL relative to the main axis ofastigmatism using the first astigmatism correcting power, the secondastigmatism correcting power, and the magnitude of astigmatism.

In some embodiments, the method further involves identifying theoff-axis position of the relaxing incision by determining the positionof the astigmatism-correcting axis of the relaxing incision relative tothe main axis of astigmatism using the first astigmatism correctingpower, the second astigmatism correcting power, and the magnitude ofastigmatism.

In some embodiments, the position of the astigmatism-correcting axis ofthe IOL, the position of the astigmatism-correcting axis of the relaxingincision, or both are determined using the law of cosines. In someembodiments, the astigmatism-correcting axis of the IOL is less than 180degrees relative to the main axis of astigmatism, and the astigmatismcorrecting axis of the relaxing incision is more than 180 degreesrelative to the main axis of astigmatism to be corrected. In someembodiments, the astigmatism-correcting axis of the IOL is more than 180degrees relative to the main axis of astigmatism, and theastigmatism-correcting axis of the relaxing incision is less than 180degrees relative to the main axis of astigmatism to be corrected.

In some embodiments, the relaxing incision intersects one or moremeridians distinct from one or more meridians intersecting an incisionfor IOL implantation.

In some embodiments, the first astigmatism correcting power, theoff-axis position of the toric IOL, the second astigmatism correctingpower, the off-axis position of the relaxing incision, or anycombination thereof is identified using a pair of vectors, the vectorsum of which comprises a magnitude and direction approximating themagnitude and axis of the astigmatism to be corrected, wherein: (a) onevector of the pair of vectors has a magnitude that corresponds to theastigmatism correcting power of the IOL and an angle, relative to thevector sum, that is twice the angle of the off-axis position of the IOL;and (b) the other vector of the pair has a magnitude that corresponds tothe astigmatism correcting power of the relaxing incision and an angle,relative to the vector sum, that is twice the angle of the off-axisposition of the relaxing incision.

In some embodiments, the tonic IOL-relaxing incision combinationprovides a theoretical residual astigmatism of less than about 0.5diopters. In some embodiments, the toric IOL-relaxing incisioncombination provides a theoretical residual astigmatism approaching 0diopters.

In another aspect, the invention provides a method for determining apost-operative corrective lens prescription for an astigmatic eye thatinvolves determining the difference between (a) the magnitude anddirection of the astigmatism to be corrected, and (b) the magnitude anddirection of the vector sum as described herein, wherein the differencecorresponds to the post-operative corrective lens prescription for theastigmatic eye. In some embodiments, the astigmatism to be correctedincludes surgically induced astigmatism. In some embodiments, themagnitude of the vector sum includes the effective astigmatismcorrecting power of the lens at the corneal plane.

In another aspect, the invention provides a corrective lens having aprescription determined as described herein.

In another aspect, the invention provides a method for marking the eyethat involves receiving the toric IOL-relaxing incision combinationidentified as described herein, and marking on the eye, the position ofthe astigmatism correcting axis of the IOL, the position of theastigmatism correcting axis of the relaxing incision, or both positionsof the astigmatism correcting axes.

Any feature or combination of features described herein are includedwithin the scope of embodiments of the present invention provided thatthe features included in any such combination are not mutuallyinconsistent as will be apparent from the context, this specificationand the knowledge of one of ordinary skill in the art.

Unless otherwise defined, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this invention belongs. In case of conflict, thepresent specification, including definitions, will control. In addition,the materials, methods, and examples are illustrative only and notintended to be limiting. Although methods and materials similar orequivalent to those described herein can be used to practice theinvention, suitable methods and materials are described below.

All patents and publications referenced or mentioned herein areindicative of the levels of skill of those skilled in the art to whichthe invention pertains, and each such referenced patent or publicationis hereby incorporated by reference to the same extent as if it had beenincorporated by reference in its entirety individually or set forthherein in its entirety. Applicants reserve the right to physicallyincorporate into this specification any and all materials andinformation from any such cited patents or publications.

Other features and advantages of the invention will be apparent from thefollowing detailed description and from the claims.

BRIEF DESCRIPTION OF THE FIGURES

FIGS. 1A-1J are graphical representations of the vector addition methodthat can be use to select the astigmatism correcting power and locationsof toric IOL and relaxing incision for an amount of astigmatism andlocation to be corrected in which each of FIGS. 1A-1J represents apossible solution for given astigmatism “A”.

FIG. 2 is a geometric representation of a method of the of the inventionfor determining astigmatism correcting powers and off-axis locations fora toric IOL-relaxing incision combination to correct a given level ofastigmatism.

FIGS. 3A-3B are schematic diagrams of on-axis (3A) and off-axis (3B)placement of toric IOL-relaxing incision combinations.

FIG. 4 illustrates a calculator system accordingly to an embodiment ofthe present invention.

FIGS. 5-11 illustrate the graphical user interface of the calculatortool that can be used to select one or more toric IOLs or relaxingincision.

FIG. 12 illustrates a method for selecting one or more toric IOLs from adatabase of lenses as disclosed herein.

DETAILED DESCRIPTION OF THE INVENTION

The invention provides methods, tools, and systems for selectingintraocular lens (IOL), relaxing incision, and IOL-relaxing incisioncombinations effective for correcting astigmatism. The methods, toolsand systems of the invention do not require alignment with the main axisof astigmatism to be corrected and allow for positions of astigmatismcorrection that do not overlap with positions of cataract incisions.

In one embodiment, the invention provides a method of performing asurgical procedure for correcting astigmatism. Astigmatism in an eye canbe corrected by identifying the magnitude and axis of astigmatism to becorrected, performing an implantation of a toric intraocular lens (IOL)in the eye at a first off-axis position in combination with relaxingincision in the limbus or cornea of the eye at a second off-axisposition.

Corneal or lenticular astigmatism refers to differing curvature ofdifferent meridians of the anterior or posterior surface of the corneaor the lens that result in impaired vision. Astigmatism can beinherited, develop over time, develop in association with diseases suchas keratoconus, or occur as a result of surgery. The term “astigmatism,”as used herein, refers to a distortion in the shape of the cornea orlens that results from or is associated with eye surgery, a diseaseaffecting the eye, or the natural shape of the cornea or lens, and thusincludes corneal astigmatism, lenticular astigmatism, as well aspre-operative astigmatism and surgically induced astigmatism (e.g. dueto cataract surgery). Thus, the astigmatism to be corrected in anexemplary method of the invention can be the net astigmatism resultingfrom pre-operative and surgically induced astigmatism, and astigmatismis corrected by a method of the invention if astigmatism determinedusing methods known to those skilled in the art is shown to be reducedor if vision acuity related to astigmatism reduction is improved by adetectable amount.

An astigmatism to be corrected can be identified and measured using anymethods and tools known to those skilled in the art for detecting andmeasuring astigmatism. Non-limiting examples include retinoscopy orautorefraction (e.g. to determine refractive error), manual refractionusing a phoropter (e.g. to determine magnitude and axis), wavefront(aberrometry) refraction, keratometry (e.g., measuring curvature of thesteepest and flattest meridians using a keratometer), and topography(e.g. determining shape using a corneal topographer). See for example,Alpins N. & Stamatelatos G. (2014) Measuring Astigmatism, PlanningSurgery and Tracking Results. In Limbal Relaxing incision, A PracticalGuide. Nichamin L and Parekh P Editors. Slack Inc.

Astigmatism to be corrected can be identified by its magnitude (i.e.amount) in diopters (D) and its orientation defined by the location ofits steep axis. As used herein, the term “axis of astigmatism,” “mainaxis,” “main axis of astigmatism,” refers to the steep axis ofastigmatism to be corrected.

In a method of the invention, astigmatism can be corrected by implantinga toric IOL in an off-axis position, i.e., a position that does notalign with the identified main axis of astigmatism (i.e. the main axisof astigmatism to be corrected). Toric IOLs are well known to thoseskilled in the art and can be obtained from various sources including,for example, Alcon Labs (Fort Worth, Tex.), Staar Surgical (Monrovia,Calif.), Abbott Medical Optics, Inc. (Santa Ana, Calif.), Bausch & Lomb(Bridgewater, N.J.), Carl Zeiss Meditec (Jena, Germany), and Physiol(Liege, Belgium). Toric IOLs can be implanted inside the eye to replacethe eye's natural lens to correct astigmatism, nearsightedness orfarsightedness or without removing the natural lens as a “phakic IOL.”Toric IOLs are constructed with meridians or axis having differentastigmatism correcting powers or cylinder powers measured in diopters(D). Non-limiting examples of astigmatism correcting powers provided bytoric IOLs include those having cylinder power about (i.e., within 15%of, or + or −15% of) 0.25, about 0.5, about 0.75, about 1, about 1.25,about 1.5, about 1.75, about 2, about 2.25, about 2.5, about 2.75, about3, about 3.25, about 3.5, about 3.75, about 4, about 4.25, about 4.5,about 4.75, about 5, about 5.25, about 5.5, about 5.75, about 6, about6.25, about 6.5, about 6.75, about 7, about 7.25, about 7.5, about 7.75,about 8, about 8.25, about 8.5, about 8.75, about 9, about 9.25, about9.5, about 9.75, or about 10 diopters at the IOL plane, each of whichhas a cylinder power at the corneal plane of about ⅔ the cylinder powerat the IOL plane. The exact ratio of astigmatism at the IOL plane toastigmatism at the corneal plane may vary, and this ratio can bedetermined using a method of the invention and is detailed in whatfollows.

A toric IOL is identified by its astigmatism correcting power (cylinderpower) at an identified axis on the IOL (cylinder axis). The cylinderaxis identified on the toric IOL allows for alignment of the toric IOLrelative to the axis of astigmatism to be corrected to facilitatepositioning the IOL at a select orientation inside the eye for optimalastigmatism correction. A toric IOL is in rotational alignment with thesteep or main axis of astigmatism if the toric IOL is positioned so thatits cylinder axis is on the steep or main axis of astigmatism thusreducing or neutralizing it. The cylinder axis of a toric IOL is theaxis of least toricity on the toric IOL. As such, the cylinder axis isthe astigmatism-correcting axis. A toric IOL is in an “off-axis”position if its cylinder axis is oriented at an angle that is not zeroor 180 degrees relative to the main or steep axis of astigmatism. Theoff-axis position of the toric IOL can be identified in degrees bymeasuring the angle between the cylinder axis of the toric IOL and themain or steep axis of astigmatism to be corrected. Methods forimplanting a toric intraocular lens (IOL) are known to those of skill inthe art. See, for example Novis, C., Astigmatism and Toric IntraocularLenses, Current Opinion in Ophthalmology, (1), 47-50 (2000).

A relaxing incision is a small arcuate incision or a pair of arcuateincisions made at the edge or opposite edges, respectively, of thecornea or limbus of the eye to relax the curvature of the cornea. Arelaxing incision functions to relax or reduce the curvature of thecornea in the meridian intersecting the incision. A relaxing incisionformed by a pair of oppositely placed, arcuate incisions relaxes orreduces the curvature of the cornea particularly along the meridianconnecting the centers of the arcuate incisions. As relaxing incisioncan be formed at the cornea or limbus, the term “relaxing incision”include corneal relaxing incision and limbal relaxing incision. Relaxingincision can be formed using a knife, for example, a diamond knife, or alaser, for example, femtosecond laser as known to those of skill in theart. See, for example, Nichamin, L. D. Nomogram for limbal relaxingincision. Journal of Cataract & Refractive Surgery, 32(9), 1408 (2006);Nichamin, Louis D. (Eds.) Limbal Relaxing incision: A Practical Guide.2014. Thorofare, N J: Slack Incorporated; and Donnenfeld, E., &Rosenberg, E. Assisting Femto Incisions with Nomograms. OphthalmologyManagement, 19 (June 2015), 48-52 (2015).

Relaxing incision can be identified by their astigmatism correctingpowers and locations. The astigmatism correcting power of a relaxingincision is determined though incision arc length as known to thoseskilled in the art. Non-limiting examples of astigmatism correctingpower (in diopters) for incisions of various lengths are provided in thetable below based on the original Donenfeld “DONO” nomogram and morerecently modified for femtosecond laser corneal incisions.

Limbal RI- Femtosecond Laser Diopters Donnenfeld Nomogram RI Nomogram0.5 1 incision, 1½ clock hrs 1 incision, 1 clock hr (45° each) (30°each) 0.75 2 incisions, 1 clock hr 2 incisions, ⅔ clock hrs (30° each)(20° each) 1.50 2 incisions, 2 clock hrs 2 incisions, 1&⅓ clock hrs (60°each) (40° each) 3.00 2 incisions, 3 clock hrs 2 incisions, 2 clock hrs(90° each) (60° each) *Use 5° more for against-the-rule astigmatism andyounger patients and 5° less for older patients

The location of relaxing incision is defined by a trans-corneal axisthat intersects the arc center of an arcuate incision or intersects thearc centers of the pair of arcuate incisions. The location or placementof relaxing incision defines the axis of astigmatism corrected by therelaxing incision or the astigmatism-correcting axis, e.g. atrans-corneal axis extending between the arc centers of a pair ofincisions.

Selecting Astigmatism Correcting Power and Off-Axis Positions of ToricIOLs and Relaxing Incision

The present disclosure provides a method for selecting combinations oftoric IOLs and relaxing incision to correct astigmatism. The astigmatismcorrecting power of the toric IOL, the astigmatism correcting power ofthe relaxing incision, as well as the location or orientation of thetoric IOL and relaxing incision can be determined prior to or at thetime of the surgery. The magnitude (or amount) and location ofastigmatism to be corrected can be identified using methods known tothose skilled in the art. As discussed above, the astigmatism to becorrected can include pre-operative as well as surgically inducedastigmatism or their combination. The astigmatism to be corrected can bea measured value, as well as an estimated value that accounts forastigmatism occurring as a consequence of incision formed duringsurgery, for example, during cataract surgery or for lens implantation.

Using the magnitude and position of the astigmatism to be corrected, thetoric IOLs and relaxing incision can be determined so that theirastigmatism correcting power and locations with respect to the main axisof astigmatism satisfies the triangle inequality theorem. Morespecifically, the magnitude of the astigmatism to be corrected and themagnitudes of the toric IOL and relaxing incision to be used are threevalues having a mathematical relationship equivalent to the mathematicalrelationship among the lengths of the sides of a triangle, inparticular, the combined lengths of any two sides of a triangle isalways longer than the third side. As such, the following triangleinequality (formula I and II) can be used to select the combination oftoric IOLs and relaxing incision effective to correct astigmatism ofmagnitude A. The triangle inequality useful in a method of the inventioncan be expressed as follows:

|L−R|<A<L+R  (I)

In equation I, the symbol | | denotes the absolute value of thedifference between L and R (i.e. L−R); L is the magnitude of theastigmatism correcting power of the lens in diopters (D), at the cornealplane; R is the magnitude of the astigmatism correcting power of therelaxing incision in diopters (D); A is the magnitude of the astigmatismto be corrected in diopters (D); and A, L and R are all positive realnumbers.

For all values of L that are greater than R (i.e. L>R), the triangleinequality can be expressed as follows:

L−R<A<L+R  (IIa)

Similarly, if R>L then the triangle inequality can be expressed as

R−L<A<L+R  (IIb)

And if L=R then the triangle inequality can be expressed as:

0<A<L+R  (IIc)

Astigmatism having magnitudes represented by values of A satisfying thetriangle inequality expressed as equation I or IIa, IIb and IIc can beneutralized or countered by positioning the astigmatic reductioncomponents, namely a toric IOL of contribution L and relaxing incisionof contribution L, obliquely relative to the main axis of astigmatism.

The specific positions of the toric IOL and relaxing incision relativeto the main axis of astigmatism can be determined using cosine and sinelaws for a triangle illustrated in FIG. 2. Triangle 30 includes sideshaving lengths L₁₁, R₁₁ and A. If the astigmatism to be corrected has amagnitude of A, then the astigmatism correcting components (thecombination of a toric IOL and relaxing incision) can have magnitudescorresponding to the values of L₁₁ and R₁₁. The off-axis positions ofthe astigmatism correcting components relative to the main axis ofastigmatism to be corrected (i.e. A) can be determined by solving forangles 2λ and 2ρ of FIG. 2, and their positions relative to the mainaxis of astigmatism in degrees are the measures of λ and ρ.

The measures of angles λ and ρ are given by:

$\begin{matrix}{\lambda = {0.5\mspace{11mu} {{ArcCos}\left\lbrack \frac{\left( {L^{2} + A^{2} - R^{2}} \right)}{2{AL}} \right\rbrack}}} & ({III}) \\{\rho = {0.5\mspace{14mu} {{ArcCos}\left\lbrack \frac{\left( {R^{2} + A^{2} - L^{2}} \right)}{2{AR}} \right\rbrack}}} & ({IV})\end{matrix}$

Those cases where the triangle inequality represented by formulas I andII is barely violated i.e. A=L−R or A=L+R, correspond to flat “line”triangles. Surgically, these represent the combination of toric IOLcontribution and relaxing incision contributions placed in parallel or“on axis” relative to the main axis of astigmatism to be corrected wheretheir contributions become additive, or perpendicularly where thecontribution add up but with a minus sign.

Combinations of toric IOLs and relaxing incision effect to correct aselect astigmatism can be identified using vector principles applicableto the addition of two vectors, the sum of which correspond to themagnitude and direction of the astigmatism to be corrected. Morespecifically, the magnitude and location of the astigmatism to becorrected can be taken as the components of a resultant vector sum oftwo vectors: one of which corresponds to the astigmatism correctingcontribution of a toric IOL and the other corresponds to the astigmatismcorrecting contribution of a pair of relaxing incision.

In sum, L and R represent the magnitudes of a first vector and a secondvector, respectively, of a vector pair, whose sum corresponds to thevector with magnitude A (the magnitude of astigmatism to be corrected).The angles of the first and the second vectors relative to vector withmagnitude A are denoted by 2λ and 2ρ, respectively. The values of 2λ and2ρ can be used to determine the off-axis locations of the toric IOL andthe relaxing incision, relative to the main astigmatism to be corrected,as λ and ρ are the angles of the astigmatism correcting axes of thetoric IOL and relaxing incision (the astigmatism correcting axis of thetoric IOL being its cylinder axis, and the astigmatism correcting axisof the relaxing incision being defined by a trans-corneal lineconnecting the arc centers of a pair of arcuate incisions formed atopposite edges of the cornea).

FIGS. 1A-1F are graphical interpretations of a method of the invention.The figures provide a Cartesian plane in which the astigmatism to becorrected is represented by vector with magnitude A on the X-axis havinga direction indicated by the arrow. To identify combinations of toricIOLs and relaxing incision effective to counter the astigmatism to becorrected, a first set of nested, concentric circles 10, having radiicorresponding to discrete astigmatism correcting powers of availabletoric IOLs (L) can be overlayed at one end (the origin or tail) of thevector with magnitude A, and a second set of nested, concentric circles20, with radii corresponding to discrete astigmatism correcting powersof defined relaxing incision (R) can be overlayed at the other end (thetip) of the vector with magnitude A. Thus, the magnitude of astigmatismto be corrected represented by the letter A is the distance between theorigins of the concentric circles 10 and 20, the radius of each circle10 represents a possible value of L (magnitude or astigmatism correctingpower of a toric IOL), and the radius of each circle 20 represents apossible value of R (magnitude or astigmatism correcting power ofrelaxing incision). The points of intersections between a circle fromeach of set 10 and 20 shown in FIGS. 1A-1F represent possiblecombinations of L and R effective to correct astigmatism represented byvector with magnitude A, as they mark the end of a first vector (ofmagnitude L) beginning at the origin of circle set 10, and the beginningof a second vector (of magnitude R) ending at the origin of circle set20. And each point of intersection of the two circles represents aparticular solution combination (a particular astigmatism correctingpower of toric IOL at an off-axis position, and a particular astigmatismcorrecting power of relaxing incision at another off-axis position) thatyields zero residual astigmatism, or the desired amount of astigmatismto be corrected as incorporated in A.

Where the circles in FIGS. 1A-1J do not intersect, the values of A, Rand L do not satisfy the triangle inequality theorem. That is, thecombined the radii of the circles is either “too small” to bridge thegap of the astigmatism A, or one of them is “too large” and goes wellbeyond the point of compensating for the astigmatism A with the othercomponent being unable to restore the “overshoot” of the firstcorrecting term.

In sum, in a method of the invention, the astigmatism correcting powerof the toric IOL and that of the relaxing incision, and the magnitude ofthe astigmatism to be corrected, are related as the magnitudes of afirst and second vector and the magnitude of their vector sum,respectively. The astigmatism correcting axis (cylinder axis) of thetoric IOL and that of the relaxing incision, measured from the axis ofastigmatism to be corrected, are about half the measures of the anglesof the first and the second vector relative to their vector sum,respectively. As such, the toric IOL (and its astigmatism correctingpower) and that of the relaxing incision, as well as their positionsrelative to the axis of astigmatism to be corrected are selected so that(1) the toric IOL has a magnitude and position that correspond to themagnitude of a first vector having a first direction, (2) the relaxingincision have an astigmatism correcting power and direction thatcorrespond to the magnitude of a second vector having a seconddirection, (3) the first and second vectors have a vector sum comprisinga magnitude that correspond to the magnitude of the astigmatism to becorrected, and (4) the first and second vectors each having a directionthat, when measured as an angle relative to the direction of the vectorsum, is twice the angle of the off-axis position of the lens andincisions, respectively.

The invention provides a method to identify a plurality of tonicIOL-relaxing incision combinations that can be used to correctastigmatism of a known magnitude. The plurality of toric IOL-relaxingincision combinations allows the surgeon to select a particularcombination of toric IOL-relaxing incision pairs most suitable for aparticular astigmatic eye. For example, the methods of the invention canbe used to determine the astigmatism correcting power of eachastigmatism-correcting component in the toric IOL-relaxing incisioncombination, as well as the position of each component with respect tothe main axis of astigmatism. As the toric IOL and relaxing incision areused in combination to apply off-axis correction of astigmatism in theeye, the toric IOL and relaxing incision are placed one on each side ofthe axis of astigmatism to be corrected, the positions of the toric IOLand relaxing incision on either side of the axis of astigmatism beinginterchangeable. For example, the toric IOL can be located in a positionthat is counter-clockwise from the main axis of astigmatism to becorrected, and the relaxing incision clockwise relative to the axis ofastigmatism. Alternatively, the relaxing incision can be placed in aposition that is counter-clockwise from the main axis of astigmatism tobe corrected, and the toric IOL in a position clockwise relative to theaxis of astigmatism. The counter-clockwise or clockwise position of thetoric IOL and relaxing incision can be selected based on a variety offactors including: (1) level of comfort or reliability; and (2) locationof cataract incision or an incision made for lens implantation oranother reason. Toric IOL-relaxing incision combinations in which theastigmatism correcting components have similar astigmatism correctingpowers are useful to minimize the disadvantages associated with oneastigmatism-correcting component. Toric IOL-relaxing incisioncombinations in which the location of one astigmatism-correctingcomponent does not overlap with another incision, e.g. cataractincisions or incisions for lens implantation, are useful in order toavoid complications associated with overlapping incisions. As usedherein, the term overlapping incisions refer to incisions that intersectat least one common meridian of the eye. Overlapping incisions areillustrated in FIG. 3A for cataract incision 44 and the relaxingincision component 48 a. In contrast, cataract incision 44 do notoverlap with relaxing incision component 48 a in FIG. 3B.

A method for identifying toric IOL-relaxing incision combinations foruse in off-axis correction disclosed herein can be used to achieveresidual astigmatism lower than typically achievable using on-axistreatment methods. For example, toric-IOL-relaxing incision combinationsidentified herein can be used in an off axis method to achieve atheoretical residual astigmatism of less than 0.4 diopters, for example,less than 0.3, 0.2, 0.1, 0.05, and near 0.04 diopters. The residualastigmatism value can be used to provide a customized, post-operativeprescription for corrective lens for the treated eye using methods knownto those skilled in the art.

The present disclosure also provides a method for preparing the eye forcorrection of astigmatism. Once a toric IOL-relaxing incisioncombination are obtained, their off axis positions relative to the axisof astigmatism to be corrected can be marked on the eye using, forexample, a marking pen or inked marker, as well as tools such as amicroscope, a fixation ring, an astigmatic ruler, or an arcuate axialmarker. Methods and tools for marking the eye in preparation forperforming lens transplant or relaxing incision are known to thoseskilled in the art. See, for example, Alpins N. & Stamatelatos G. (2014)Measuring Astigmatism, Planning Surgery and Tracking Results. In LimbalRelaxing incision, A Practical Guide. Nichamin L and Parekh P Editors.Slack Inc.; Nichamin, Louis D. (Eds.) Limbal Relaxing incision: APractical Guide. 2014. Thorofare, N.J.: Slack Incorporated; and J. B.Rubenstein, Today's Peripheral Corneal Relaxing incision, in Cataract &Refractive Surgery Today, pages 26-28, May 2014.

The methods of the invention can be performed on a subject, which can beany organism within the class mammalia. Thus the term “subject” includesmembers in the orders carnivore (e.g., dogs and cats), rodentia (e.g.,mice, guinea pigs, and rats), and primates (e.g., humans, chimpanzees,and monkeys). In some embodiments, the subject is a human. The term“humans” may include human subjects of both genders and at any stage ofdevelopment (e.g., fetal, neonates, infant, juvenile, adolescent, andadult), where in certain embodiments the human subject is a juvenile,adolescent or adult. Thus, while the methods described herein may beused to perform a surgical procedure on a human subject, it is to beunderstood that the methods may also be used to perform a surgicalprocedure on other non-human subjects.

Specific embodiments of the invention are described in the followingexamples, which do not limit the scope of the invention described in theclaims.

Examples

I. Determination of Astigmatism Correcting Power and Position for LensImplantation and Relaxing Incision Placement

Vector addition is used to determine possible combinations of (a)astigmatism correcting power of a toric IOL, (b) position of the toricIOL as defined by the astigmatism-correcting axis or cylinder axis ofthe toric IOL relative to the main axis of astigmatism, (c) astigmatismcorrecting power of relaxing incision, and (d) position of the relaxingincision as defined by an trans-corneal axis passing through the centersof the arcuate relaxing incision (i.e. arc centers) relative to the mainaxis of astigmatism.

The astigmatism to be corrected having diopters of about 1.9 is plottedon the x-axis as as vector with magnitude A=1.9 as shown in FIGS. 1A-1J.Existing toric IOLs with discrete diopter values of 1.03 diopters, 1.54diopters and 2.06 diopters, for example, are plotted as solid circles10, their centers coinciding with origin of the astigmatism vector atthe origin of the Cartesian plane. Each of the three circles 10 has aradius that corresponds to the astigmatism correcting power in dioptersof an existing toric IOL. Defined relaxing incision with effectivediscrete diopter values 0.75 and 1.50 are plotted as circles 20, theircenters coinciding with the tip of astigmatism vector at 1.9 on thex-axis. The ten points of intersection formed by a circle 10 and acircle 20 (see FIGS. 1A-1J) correspond to ten possible toricIOL-relaxing incision combinations having magnitudes and positionseffective to correct astigmatism of 1.9 diopters as summarized in thetable below.

Solution Toric IOL Relaxing incision Combination Power^(#) Location*Power^(##) Location**  1 (FIG. 1A) 1.03 D   25.9° 1.50 D −16.3°  2 (FIG.1B) 1.54 D   25.2° 1.50 D −26.1°  3 (FIG. 1C) 2.06 D   22.1° 1.50 D−36.8°  4 (FIG. 1D) 1.54 D   11.1° 0.75 D −25.4°  5 (FIG. 1E) 2.06 D  10.7° 0.75 D −45.7°  6 (FIG. 1F) 1.03 D −25.9° 1.50 D   16.3°  7 (FIG.1G) 1.54 D −25.2° 1.50 D   26.1°  8 (FIG. 1H) 2.06 D −22.1° 1.50 D  36.8°  9 (FIG. 1I) 1.54 D −11.1° 0.75 D   25.4° 10 (FIG. 1J) 2.06 D−10.7° 0.75 D   45.7° ^(#)astigmatism correcting power of the toric IOLat the corneal plane *location of cylinder axis relative to the mainaxis of astigmatism to be corrected ^(##)astigmatism correcting power ofthe limbal or corneal relaxing incision **location of astigmatismcorrecting axis relative to the main axis of astigmatism to be corrected

The graphical representations shown in FIGS. 1A-1H illustrate aplurality of solutions for correcting astigmatism of 1.9 diopters. Andfor each toric-IOL-relaxing incision combination, two possiblearrangements of the toric IOL and relaxing incision are possible, asindicated by two points of intersection of the same two circles, oneabove the axis and one below the x-axis. One arrangement corresponds tothe toric IOL being on a first side of the main astigmatism axis, e.g.clockwise relative to the main axis of astigmatism, and the relaxingincision being on the other side, e.g., counter-clockwise, of the mainaxis of astigmatism. The second arrangement corresponds the relaxingincision being on a first side of the main axis of astigmatism, e.g.clockwise relative to the main axis of astigmatism, and the toric IOLbeing on the other side, e.g. counter-clockwise, of the main axis ofastigmatism. For example, each solution pairs illustrated in FIGS. 1Aand 1F, FIGS. 1B and 1G, FIGS. 1C and 1H, FIGS. 1D and 1I, and FIGS. 1Eand 1J represent astigmatism correcting contributions of L and R thathave similar magnitudes but opposite directions. In FIG. 1A, the angleof L can be consider positive and that of R negative, as L and R areabove the x-axis (the main axis of astigmatism). In FIG. 1F, the angleof L can be consider negative and that of R position, as L and R arebelow the x-axis. FIGS. 1A and 1F indicate that for each toricIOL-relaxing incision combination, the toric IOL and relaxing incisioncomponents can be arranged in two ways relative to the main axis ofastigmatism. In one arrangement, the toric IOL is clockwise, whilerelaxing incision is counter-clockwise, relative to the main axis ofastigmatism. In the other arrangement, the relaxing incision isclockwise, while the toric IOL is counter-clockwise, relative to themain axis of astigmatism. The ability to reverse the placement of thetoric IOL and relaxing incision allows the surgeon to avoid formingrelaxing incision that radially overlap with cataract incisions orincisions made for lens implantation, i.e. relaxing incision intersectone or more meridians of the eye that are distinct from the one or moremeridians that intersect a cataract incision or incision made for anyother purpose.

II. Off-Axis Implantation of a Toric IOL in Combination with Off-AxisPlacement of Relaxing Incision to Maximizse Range of AstigmatismCorrection

Astigmatisms of various diopters are corrected though modifying theoff-axis orientation of a particular toric IOL-relaxing incisioncombination as follows. A toric IOL having an astigmatism correctingpower of about 2.00 diopters at the corneal plane, for example, theAlcon “T5” (SN6AT5) or its equivalent, combined with relaxing incisionhaving an astigmatism correcting power of about 1.5 diopters (DONONnomogram) potentially corrects astigmatism (in diopters) between amagnitude range as follows:

2.00−1.5<A<2.00+1.5

0.50<A<3.50

Positioning the astigmatism correcting axes of the toric IOL and therelaxing incision in close proximity to the main axis of astigmatismcorrects astigmatism approaching 3.5 diopters, while placing theastigmatism correcting axes of the toric IOL along the main axis and therelaxing incision approaching 90 degrees from the main axis ofastigmatism to be corrected neutralizes astigmatism to an magnitudeapproaching 0.5 diopters.

A significant majority of patients presenting for cataract surgery withastigmatism deemed correctable with good outcome falls within the rangeof 0.50 and 3.50 diopters.

The following table illustrates possible amounts of astigmatismcorrectable by such a combination and the corresponding angles.

A Toric IOL angle* RI angle* 0.9 + or − 22.3° − or + 55.2° 1.4 + or −24.3° − or + 43.6° 1.9 + or − 22.6° − or + 35.5° 2.4 + or − 19.3° − or +28.1° 2.9 + or − 14.4° − or + 20.0° 3.4 + or − 5.9° − or + 7.9° *Whenthe toric IOL angle is a positive value, the RI angle is a negativevalue. And when RI angle is a positive value, the toric IOL angle is anegative value.

As the of astigmatism-correcting axis of the toric IOL and that of therelaxing incision are positioned on different sides of the main axis ofastigmatism, one in a counter-clock wise position and the other in aclock-wise position relative to the main axis of astigmatism, eachcombination of toric IOL-relaxing incision will include an astigmatismcorrecting component with a position indicated by a positive angle and acomponent with a position indicated by a negative angle.

As clear from the preceding description the angle of tIOL represents theposition of the tIOL on one side of the axis of main astigmatism and theangle of RI is on the other side. Each row in the table or pairs ofangles corresponds thus to two distinct possible surgical choices.

III. Use of Off-Axis Implantation of a Toric IOL in Combination withOff-Axis Placement of Relaxing Incision to Minimize Residual Astigmatism

This example illustrates the residual astigmatism achievable under amethod of the invention. The patient has cataract in the right eye andcornea astigmatism given by 43.00 @ 73 and 45.00 @ 163 with a customarysurgical induced astigmatism (SIA) of 0.20 D measuring one clock hourand centered at 210. Thus, the magnitude of astigmatism to be correctedis 2.00 diopters (45-43) at the steep axis (163 degrees) prior toaccounting for SIA, and 1.95 diopters at 160 degrees after accountingfor SIA (the cross cylinder or sum of corneal astigmatism and SIA). Thesurgeon is right handed and takes a temporal approach to the cataractsurgery. The position of the surgeon is therefore at 180 degrees and theright hand uses a keratome that incises the cornea about 20 degrees tothe right for a location of the cataract incision at 200 degrees. Forthis surgeon, an incision of about 2.4 mm results in an SIA of 0.20diopters. This is entered in the Alcon toric calculator, UniversIOLcalculator or any other calculator that combines astigmatism. Theresults are shown in the output of the Alcon calculator below.

The table below provides the astigmatism correcting power in diopters(D) of available toric IOLs (Alcon SN6ATx)—at the IOL plane and at thecorneal plane. The Sn6ATx IOL is represented by a corresponding x in thetable.

T IOL Plane Corneal Plane 3 1.5  1.03 4 2.25 1.54 5 3.00 2.06 6 3.752.57 7 4.50 3.08 8 5.25 3.60 9 6.0  4.11

Based on the patient's cornea astigmatism, a T4 toric IOL withastigmatism correcting power of 1.54 diopters at the corneal plane isindicated. With on-axis implantation, residual astigmatism is estimatedto be about 0.40 diopters when computed using the Alcon ToricCalculator.

FIG. 3A is a schematic representation of the on-axis positions of thetoric IOL and relaxing incision relative to the location of the cataractincisions. In this case, forming relaxing incision on the main axis ofastigmatism results in overlap of the cataract incision with the limbalrelaxing incision. Overlapping of the incisions can cause gaping andedema, in addition to making the results less predictable, is consideredundesirable by a majority of surgeons and is cannot be computed bymainstream LRI calculators such as LRIcalculator.com.

As the residual astigmatism after implantation of the toric IOL is 0.40diopters, neither the DONO nor the NAPA nomograms provides for acompensating relaxing incision, as the minimum astigmatism correctingpower is 0.50 diopters for DONO and 0.75 diopters for NAPA. For example,the LRIcalculator.com, which offers an implementation of some of thesenomograms, rejects requests to compute LRIs corresponding to this amountof astigmatism. While implanting a toric IOL having a lower astigmatismcorrecting power may allow for determining a relaxing incisioncontribution, one incision of the pair of relaxing incision may overlapor be very close to the location of the cataract incision and may notconstitute a feasible or desirable option.

A toric IOL of the same astigmatism correcting power (1.54 diopters) isimplanted in the eye in combination with relaxing incision of 1.50diopters at off-axis positions as illustrated in FIG. 3B according to amethod of the invention. The off-axis positions of the toric IOLs andrelaxing incision are determined according to the triangle inequalitymethods of the invention, for example, as illustrated in FIG. 1B.Implantation of the toric IOL (1.54 diopters) at about 25 degreescounter-clockwise from the main axis of astigmatism to be corrected(location of cylinder axis to main axis of astigmatism to be corrected)in combination with placement of the relaxing incision about 25 degreeson the other side (clockwise) of the main axis of astigmatism to becorrected enables complete astigmatism correction, i.e. yielding atheoretical residual astigmatism approaching 0 degrees or of 0 degrees.

The oblique placement angle of the relaxing incision and/orinterchangeability of the location of toric IOL and relaxing incisionallow for surgical solutions that avoid overlap between cataractincisions and relaxing incision. As shown in FIG. 3B, the toric IOL isimplanted at an off-axis angle λ occurring counter-clockwise to the mainaxis of astigmatism, its astigmatism correcting axis (cylinder axis) 46being positioned between cataract incision 44 and main axis ofastigmatism 42, while relaxing incision components 48 a and 48 b areplaced on the other side (clockwise) of main axis of astigmatism 42, itsastigmatism correcting axis 48 (trans-corneal line connecting the arccenters of the opposite, arcuate incisions) being at an oblique,off-axis angle ρ.

The resulting residual astigmatism approaching 0 is confirmed using avector calculator available at http://www.1728.org/vectors.htm and thefollowing vector components inputs.

Vector Magnitude Direction 1-Astigmatism 1.95 diopters  0 degrees2-toric IOL 1.55 diopters 230 degrees 3-relaxing incisions  1.5 diopters130 degrees

Vector 1 corresponds to astigmatism to be corrected and is designated asbeing at 0 degrees. As vectors 2 and 3 represent astigmatism-correctingcomponents, their contributions acting to neutralize or counterastigmatism, their directions are opposite of vector 1 and thusdetermined relative to the position that is 180 degrees from thedirection of astigmatism represented by vector 1 (0 degrees). And asvectors 2 and 3 are at oblique angles occurring on either side of theaxis of astigmatism, their angle components being twice that of theoff-axis angles of the toric IOL and relaxing incision, the anglecomponents of vector 2 and 3 are computed as the sum and difference,respectively, of twice the off-axis angles of the toric IOL and relaxingincision as follows:

Angle of vector 2=180+(2*25 degrees); and  (V)

Angle of vector 3=180−(2*25 degrees).  (VI)

Thus, the angle of vector 2 (with represents the toric IOL contribution)is 230 degrees relative to the main axis of astigmatism (0 degrees), andthe angle of vector 3 (which represents the contribution of the relaxingincision) is 130 degrees relative to the main axis of astigmatism (0degrees). These inputs yield a residual astigmatism of 0.039716 diopterswhen computed using the vector calculator (available athttp://www.1728.org/vectors.htm).

IV. Method of Avoiding Incisions Overlap

The following is used to determine positioning of the toric IOL andrelaxing incision in a combination so as to avoid radially overlappingincisions. The location of the main axis of astigmatism is denoted by α.The positioning of the desired toric IOL is denoted by α+/−λ, and thatof relaxing incision is denoted by α−/+ρ. The cataract incision isdenoted by iota. The arc length of relaxing incision is 2R, the arclength of the cataract incision is 2I, and β=I+R.

The 2 “limiting quantities,” L1 and L2, can be determined as follows:

L1=ι−α−β  (VIII)

L2=ι−α+β−π  (IX)

There is no overlap between a relaxing incision and the cataractincision if the value of ρ falls between L1 and L2. Similarly there isno overlap between a relaxing incision and the cataract incision if thevalue of −ρ falls between L1 and L2.

Thus, if both ρ and −ρ are within the bracket defined by L1 and L2, thenboth relaxing incision configurations are non-overlapping with thecataract incision. And if both ρ and −ρ are outside the bracket definedby L1 and L2, then both relaxing incision configurations will overlapwith the cataract incision.

The present disclosure provides a method for selecting the positions ofthe toric IOL and relaxing incision in a combination, and thus, allowsfor the inclusion or exclusion of appropriate incisions, without needfor visual intervention by a surgeon or technician.

V. Computational Tool for Selecting IOL from a Variety of AvailableLenses and Correcting Refractive Error and Astigmatism with One or MoreIOL or RI

The invention provides an intraocular lens (IOL) calculator having threemain components: front end 401, which can produce a graphical userinterface (GUI), a computational engine 402, and a database of IOLs 403.See FIG. 4. The front end 401 receives input, manually or throughcommunications with other measuring or storage devices, about one ormore eyes and their characteristic, as well as the mode of computationand preferences. Examples of devices include web-connected devices,Ultrasound (US) or partial coherence interferometry (PCI) devices, anapplication dedicated to the presently described methods or a computerdedicated to the present method. The computational engine 402 includes acore calculator and perform calculations using the input from the frontend 401, effectively selecting one or more IOLs and communicates withthe lens database 403 in order to verify the availability andsuitability of IOLs. The computational engine 402 performs ranking andfiltering operations, e.g., as described herein, before returning a listof IOLs to the front end 401 that are selected and ranked according tothe criteria specified by the user, e.g., through the front end orpreviously stored in devices connected to the front end 401, e.g., instorage configured to store criteria for ranking and filtering asdescribed herein. The computational methods include those describedherein. Other computational methods can also be used, for example, theSRKT formula and others as described in Retzlaff, J. A., Sanders, D. R.,& Kraff, M. C. (1990). Development of the SRK/T intraocular lens implantpower calculation formula. Journal of Cataract & Refractive Surgery,16(3), 333-340; Sanders, D. R., Retzlaff, J. A., Kraff, M. C., Gimbel,H. V., & Raanan, M. G. (1990). Comparison of the SRK/T formula and othertheoretical and regression formulas. Journal of Cataract & RefractiveSurgery, 16(3), 341-346; Hoffer, K. J. (1993). The Hoffer Q formula: Acomparison of theoretic and regression formulas. Journal of Cataract &Refractive Surgery, 19(6), 700-712; and Holladay, J. T., Musgrove, K.H., Prager, T. C., Lewis, J. W., Chandler, T. Y., & Ruiz, R. S. (1988).A three-part system for refining intraocular lens power calculations.Journal of Cataract & Refractive Surgery, 14(1), 17-24.

In one example, the front end 401 and the core calculator 403 caninclude circuitry for processing that is specifically configured toperform the method steps described herein.

FIG. 5 illustrates input for a calculation performed for the right eye(OD) of a patient with various filtering and ranking criteria asindicated, e.g., in a first panel 501. The input can be produced by thefront end 401, for example. The calculated values can be calculated atthe core calculator 403 and sent to the front end 401 for display, e.g.,in a second panel 502. The lower portion of the first panel 501corresponds to the biometric information, including corneal power in twomeridians and axial length with its mode of acquisition, as well assurgically induced astigmatism and its orientation.

The following include some of the possible choices corresponding tofeatures that can be selected from the database: brands, models fromeach brands, maximum lens count to be ranked, material of the implants,and focality (e.g., monofocal, bifocal, trifocal, multifocal), numberdelivery system, lens type, add power, sphericity, geometry, material,ultraviolet (UV) block, violet light filter, recommended incision sizeminimum, recommended incision size maximum, haptic angle, opticdiameter, overall diameter, edge, design, foldable, pieces, index ofrefraction, sphere minimum, sphere maximum, sphere increment, cylinderIOL plane minimum, cylinder IOL plane maximum, cylinder IOL planeincrements, toricity ratio, SRK/T nominal A constant, SRK/T optical Aconstant, SRK/T ultrasound A constant, Holladayl optical surgeon factor,Holladayl ultrasound surgeon factor, Hoffer optical constant, HofferQultrasound constant, Haigis Optical constants, and Haigis Ultrasoundconstants. References, and information about date retrieved (yy/mm/dd)are also available to the user. Information on approved regions is alsoavailable and can be used to limit the search. Corresponding images foreach lens are available.

Once initial criteria are selected, a ranked list of IOLs is generatedusing the “Select Lens” selection. In an example, the “select lens” isan actionable icon or other display device on the GUI produced by thefront end 401. FIG. 6 shows the resulting ranked list in the rightpanel, and any element can be selected with a resulting display of itsfull characteristic and a description of how it fulfills the criteriaspecified. The resulting ranted list can be produced by the corecalculator 402 using the method steps described herein, e.g., thosedescribed with reference to FIGS. 1-3. Front end 401 can display theresulting list in a bifurcated GUI with a first panel and a secondpanel. The first panel and the second panel can be distinct from eachother. The panels can be separated by a fixed graphical element, whilethe panels themselves can change. The first panel can show the settingsthat can be used determine a lens or ranking of a plurality of lenses.The inputs into the first panel can be changed. The second panel isproduced based the inputs into the first panel and in view of the rulesbeing executed in the core calculator 402. The second panel can be theright panel.

A possible list of manufacturers is illustrated in FIG. 7 and one hasbeen selected, here shown as Alcon. The possible list of manufacturesmay be a graphical element 701 that is produced from the first panelupon selection of a manufacturer's element also in the first panel. Themanufacturers can be selected or deselected at will and those settingsalong with other settings and preferences saved for subsequent sessions.

Other input elements in the first panel can also produce a graphicalelement from which an input can be selected and then used for producingthe results in the second panel.

FIG. 8 illustrates the interface for selecting criteria for lensordering. The following examples include a criterion where IOLs forwhich the Sphere portion of the correction is closest to target wouldtake preference in ranking regardless of residual astigmatism. This canbe shown in a graphical element in the first panel 501. The oppositecriterion is listed, and a “blur” criterion [Thibos] that combinessphere and astigmatism is also illustrated as a graphical element. Thislater criterion is particularly powerful in the context of combinedselection of sphere and astigmatic powers of an IOL.

The calculation of a toric IOL on a variety of other calculators istypically performed with a method of “fixed toricity ratio,” which hasbeen demonstrated to be inaccurate except for eyes of average anatomy.See, for example, Goggin, M., Moore, S., & Esterman, A. (2011). Outcomeof toric intraocular lens implantation after adjusting for anteriorchamber depth and intraocular lens sphere equivalent power effects.Archives of Ophthalmology, 129(8), 998-1003).

The present disclosure also provides a method to compute the toricityratio as follows:

1/[(1−εKf)(1−εKs)]=τ  (VII)

where ε=e/n and e is the ELP or effective lens position that iscomputable in a known manner and in various publications for differentspherical formulae. See, for example, SRK/T, Hoffer Q, Holladay 1, aslisted above. In the above formula, “n” is the index of refraction ofthe medium (mainly aqueous humor) and can be taken to be 4/3 or otherappropriate values used in the literature.

To illustrate: with Kf=Ks=40D, ε=5 mm, τ=1/0.64˜1/(⅔)=3/2=1.5, a valuevery close to the one used by Alcon online calculator (˜1.46) despitebroad approximations made here. Thus, τ will increase with increasing Kand increasing e, which in turn increases with increasing axial length.This is consistent with numerical calculations made by Savinni, Hofferet al in the context of a specific IOLformula. See Savini, G., Hoffer,K. J., Carbonelli, M. Ducoli, P & Barboni, P. Influence of axial lengthand corneal power on the astigmatic power of toric intraocular lenses.Journal of Cataract c Refractive Surgery, 39(12), 1900-1903)

In addition to a variable toricity ratio and the customary fixedtoricity ratio, a calculator disclosed herein offers a brand-specificmethod (variable if brand calculator uses variable and fixed if brandcalculator uses fixed) and a meridian based method (Fam, H. B., & Lim,K. L. Meridional analysis for calculating the expected spherocylindricalrefraction in eyes with toric intraocular lenses. Journal of Cataract &Refractive Surgery, 33(12), 2072-2076)) which can be selected as shownin FIG. 9.

To deduce the toricity ratio of a particular calculator, the followingmethod is used in which: TC=Ks−Kf is the toricity at cornea; TIOL is thetoricity at the IOL; RAK is the corneal residual astigmatism returned bythe calculator. Thus, τ=TIOL/(TC+RAK), and where τ is the toricity ratioand RAK is used with the appropriate sign.

FIG. 10 illustrates a graphical user interface, e.g., in panels 501,502, that shows a subset of a variety of calculation methods that can beused, which includes third and fourth generation methods, as well ashybrid methods to optimize outcomes and a post-LASIK method, see forexample Haigis, W. (2008). Intraocular lens calculation after refractivesurgery for myopia: Haigis-L formula. Journal of Cataract & RefractiveSurgery, 34(10), 1658-1663. A multitude of post LASIK or post refractivemethods can be included and integrated in the same calculator instead ofbeing provided only in special purpose calculator like is mostcustomary. See for example http://iolcalc.org/

This particular grouping of methods is preferable to the customarysituation where different calculation methods may be distributed amongstdifferent calculators or devices. The grouping can be shown in agraphical element in the first panel 501. These multiple methods can allbe stored in computational engine 402 and individually executed whenselected in the element in the first panel 501. The “formula spread”output is generated at the bottom right. It gives an indication of howthe formulas differ. It is equal to the absolute value of the differencebetween the highest and the lowest IOL power generated. It is a reliableindicator of the predictability of the surgical outcome when a singleformula is used for the calculation. The output graphic 1001 is in thesecond panel 502 and indicates the operated eye, incision site andpositioning of the IOL when implanted.

The sphere value of the required IOL is obtained and ported to adifferent calculator (or series of instructions in the computationalengine 402) to compute the toric information of the required implant.This is supported in the present calculator (computational engine 402)when Lens Power is selected in the Sphere Spec field as shown in FIG.11. The preferred simultaneous mode of calculation is also supported asindicated. FIG. 12 provides a summary of an example of a method forselecting toric IOL.

In addition to the foregoing features it is also possible to combine LRIand tIOL. The on-axis combination of LRI (limbal relaxing incision) orother incisional astigmatic reduction methods, collectively referred toas LRI or RI, is known to those skilled in the art. See, for example,Gills, J. P., Van Der Karr, M., & Cherchio, M. (2002). Combined tonicintraocular lens implantation and relaxing incision to reduce highpreexisting astigmatism. Journal of Cataract & Reactive Surgery, 28(9),1585-1588

The novel approach presented here is implemented by selecting from amenu for correction of astigmatism as follows. In a first step, the userselects the number of astigmatic correction devices or interventionsfrom the following choices: “0”, “1 or less”, “2 or less”, or “3 orless” astigmatic correction devices/interventions. Devices orinterventions include toric IOL, piggyback toric IOL, relaxing incision,or another intervention for reducing astigmatism or refractive error.

A section of 0 devices or interventions corresponds to no attempt atcorrecting astigmatism and will result in a non-toric IOL beingselected.

For a choice of “1 or less”, a choice of a toric IOL or a relaxingincision is offered, and the computations offer all solutions within theselected criteria that can be implemented with either a tIOL or arelaxing incision.

With a choice of “2 or less”, solutions corresponding to 0, 1 or 2devices or interventions are offered and ranked according to theselected criteria.

Examples of the use of two devices or interventions include: one toricIOL and one pair of relaxing incision as discussed above in the examplesections; two sets of relaxing incisions; or two toric IOLs, forexample, one to be implanted in the capsular bag and one to be implantedin the sulcus (piggyback).

The choice of “3 or less” proceeds in a similar manner. The methods ofcomputations are essentially identical to the ones detailed in theexamples section.

OTHER EMBODIMENTS OF THE INVENTION

While the invention has been described in conjunction with the detaileddescription, the foregoing description is intended to illustrate and notlimit the scope of the invention, which is defined by the scope of theclaims. Other aspects, advantages, and modifications are within thescope of the claims.

As used herein and in the appended claims, the singular forms “a,” “an,”and “the” include plural reference unless the context clearly dictatesotherwise. Under no circumstances may the patent application beinterpreted to be limited to the specific examples or embodiments ormethods specifically disclosed herein.

Embodiments are described herein at a level of detail to allow one ofordinary skill in the art to make and use the methods, devices, systems,etc. described herein, however, variations are possible. Components,elements, and/or steps may be altered, added, removed, or rearranged.Processing steps may be added, removed, or reordered. Variousembodiments are explicitly described herein; other possible embodimentsthat are apparent to those of ordinary skill in the art would be withinthe scope of embodiments of the present disclosure.

The present disclosure partitions devices and systems into multiplecomponents, devices or steps to facilitate understanding. One or morecomponents, devices or steps may operate as a single unit, however, andconversely, a single component, device or step can include one or moresub-components or sub-modules. The communication between the components,devices or steps can occur in a variety of ways including throughhardware implementations (e.g., over a network or internal bus),instructions in dedicated hardware, or a combination of hardware andinstructions. Such communications can use a variety of signals,protocols, and system architectures, such as, for example, radio signalsand networks. Various forms of hardware, instruction, firmware,electronic, and optical elements, as well as various combinations ofintegrated circuits can be used to implement some steps of the presentlydescribed medical methods. The integrated circuits may be part of aspecialized computing device designed to perform the particularfunctions described herein rather than by a general-purpose computer.Multiple distributed computing devices can be substituted for any onecomputing device illustrated herein, in which case, the functions of theone computing device are distributed (e.g., over a network) such thatsome functions are performed on each of the distributed computingdevices. While certain embodiments are explicitly described, otherembodiments are apparent to those of ordinary skill in the art based onthis disclosure. Therefore, the scope of the invention is defined byreference to the claims and not simply with regard to the explicitlydescribed embodiments.

What is claimed is:
 1. A method for determining a post-operative,corrective lens prescription for an astigmatic eye, the methodcomprising determining a difference between (a) the magnitude anddirection of an astigmatism to be corrected, and (b) the magnitude anddirection of a vector sum, wherein the difference corresponds to thepost-operative, corrective lens prescription for the astigmatic eye,wherein the vector sum comprises the sum of a first vector and a secondvector, and wherein: (i) the first vector comprises: (i) a magnitudethat corresponds to the astigmatism correcting power of a toricintraocular lens (IOL) placed at a first off-axis position in the eyerelative to the main axis of the astigmatism to be corrected, and (ii) afirst angle, relative to the vector sum, that is twice the angle of thefirst off-axis position relative to the main axis of the astigmatism tobe corrected; and (ii) the second vector comprises: (i) a magnitude thatcorresponds to the astigmatism correcting power of a relaxing incision(RI) placed at a second off-axis position in the eye relative to themain axis of the astigmatism to be corrected, and (ii) a second angle,relative to the vector sum, that is twice the angle of the secondoff-axis position relative to the main axis of the astigmatism to becorrected.
 2. The method of claim 1, wherein the astigmatism to becorrected comprises surgically induced astigmatism existing prior to theoff-axis toric IOL and the off-axis RI placement.
 3. The method of claim1, wherein the magnitude of the vector sum comprises the effectiveastigmatism correcting power of the lens at the corneal plane.
 4. Themethod of claim 1, further comprising incorporating the post-operative,corrective lens prescription in a corrective lens.
 5. The method ofclaim 1, wherein the corrective lens is eyeglasses.
 6. The method ofclaim 1, wherein first astigmatism correcting power is the astigmatismcorrecting power of the toric IOL at the corneal plane.
 7. The method ofclaim 6, wherein the astigmatism correcting power of the toric IOL atthe corneal plane is determined using anatomical distances within theeye.
 8. The method of claim 1, wherein the toric IOL is selected basedon residual sphere value, residual astigmatism value, the index ofrefraction of the toric IOL, or any combination thereof.
 9. The methodof claim 1, wherein the astigmatism correcting power of the toric IOL orthe astigmatism correcting power of the RI is about 0.25, about 0.5,about 0.75, about 1, about 1.25, about 1.5, about 1.75, about 2, about2.25, about 2.5, about 2.75, about 3, about 3.25, about 3.5, about 3.75,about 4, about 4.25, about 4.5, about 4.75, about 5, about 5.25, about5.5, about 5.75, about 6, about 6.25, about 6.5, about 6.75, about 7,about 7.25, about 7.5, about 7.75, about 8, about 8.25, about 8.5, about8.75, about 9, about 9.25, about 9.5, about 9.75, or about 10 diopters.10. The method of claim 1, wherein each of the astigmatism correctingpower of the toric IOL and the astigmatism correcting power of the RI isabout 0.25, about 0.5, about 0.75, about 1, about 1.25, about 1.5, about1.75, about 2, about 2.25, about 2.5, about 2.75, about 3, about 3.25,about 3.5, about 3.75, about 4, about 4.25, about 4.5, about 4.75, about5, about 5.25, about 5.5, about 5.75, about 6, about 6.25, about 6.5,about 6.75, about 7, about 7.25, about 7.5, about 7.75, about 8, about8.25, about 8.5, about 8.75, about 9, about 9.25, about 9.5, about 9.75,or about 10 diopters.
 11. The method of claim 1, wherein the astigmatismcorrecting axis of the toric IOL is less than 180 degrees relative tothe main axis of astigmatism, and the astigmatism correcting axis of therelaxing incision is more than 180 degrees relative to the main axis ofastigmatism to be corrected.
 12. The method of claim 1, wherein theastigmatism correcting axis of the toric IOL is more than 180 degreesrelative to the main axis of astigmatism, and the astigmatism correctingaxis of the relaxing incision is less than 180 degrees relative to themain axis of astigmatism to be corrected.
 13. The method of claim 1,wherein the relaxing incision intersects one or more meridians distinctfrom one or more meridians intersecting an incision for toric IOLimplantation.
 14. The method of claim 1, wherein the difference is lessthan about 0.5 diopters.